# Homework Help: Decay of Upsilon(4S) into two B mesons in laboratory frame.

1. Nov 22, 2011

### LCFC

1. The problem statement, all variables and given/known data
B mesons can be created through the reaction chain e+e- → $\Upsilon$(4S) → B+B- by colliding beams of electrons and positrons head-on at centre-of-mass energy equivalent to the mass of the $\Upsilon$(4S) resonance.

a) If the electron beam energy is 8GeV, show that a positron beam energy of 3.498GeV is required to produce a centre-of-mass energy equivalent to the mass of the $\Upsilon$(4S) resonance. Calculate the velocity β=v/c, and the Lorentz boost factor, γ, of the $\Upsilon$(4S) produced, in the laboratory frame.

b) For case (a) whare are the maximum and minimum possible B meson momenta, as measured in the laboratory frame, resulting from the decay of the $\Upsilon$(4S)?

2. The attempt at a solution

a) ECM= M($\Upsilon$(4S)) = 10.5794 GeV
s = (E1 + E2)2 - (p1+p2)2 (these momenta are vectors).

Neglect the mass of electron and positron, so E= |p|
E2 is unknown.

Therefore, s = (8+x)2 - (8-x)2

Work through to get x = 3.498 GeV as required.

β=p/E = $\frac{8-3.498}{8+3.498}$ = 0.3915

γ=1/(1-beta^2)^0.5 = 1.087

Fairly confident my answers above are correct, just not sure how to go about part b at all. Any help is really appreaciated.

Thoughts I had were to calculate the relativistic momentum and then use the cosine of the angle, the maximum value of cosine being 1 and the minimum being -1.

Last edited: Nov 22, 2011